LMFDB - Embedded newform 1824.2.bb.a.31.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1824,2,Mod(31,1824)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1824, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1824.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1824 = 2^{5} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1824.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.5647133287$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	1824.31
Dual form			1824.2.bb.a.1471.9

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.352093 - 0.609843i) q^{5} -0.0726253i q^{7} +(-0.500000 + 0.866025i) q^{9} -1.77299i q^{11} +(2.42846 + 1.40207i) q^{13} +(-0.352093 + 0.609843i) q^{15} +(3.41547 + 5.91577i) q^{17} +(-3.54782 + 2.53239i) q^{19} +(-0.0628953 + 0.0363126i) q^{21} +(4.39446 + 2.53714i) q^{23} +(2.25206 - 3.90068i) q^{25} +1.00000 q^{27} +(-5.17824 - 2.98966i) q^{29} +0.690868 q^{31} +(-1.53545 + 0.886495i) q^{33} +(-0.0442900 + 0.0255709i) q^{35} +10.7779i q^{37} -2.80414i q^{39} +(-1.04119 + 0.601130i) q^{41} +(9.49783 - 5.48357i) q^{43} +0.704186 q^{45} +(-3.35724 - 1.93830i) q^{47} +6.99473 q^{49} +(3.41547 - 5.91577i) q^{51} +(9.05207 + 5.22621i) q^{53} +(-1.08125 + 0.624257i) q^{55} +(3.96702 + 1.80630i) q^{57} +(-7.24248 - 12.5443i) q^{59} +(4.69049 - 8.12417i) q^{61} +(0.0628953 + 0.0363126i) q^{63} -1.97464i q^{65} +(1.61637 - 2.79963i) q^{67} -5.07429i q^{69} +(-1.90279 - 3.29573i) q^{71} +(5.46110 + 9.45890i) q^{73} -4.50412 q^{75} -0.128764 q^{77} +(5.68613 + 9.84867i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.2982i q^{83} +(2.40513 - 4.16581i) q^{85} +5.97932i q^{87} +(7.06701 + 4.08014i) q^{89} +(0.101826 - 0.176367i) q^{91} +(-0.345434 - 0.598309i) q^{93} +(2.79352 + 1.27197i) q^{95} +(-6.90853 + 3.98864i) q^{97} +(1.53545 + 0.886495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) $ 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1824\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$799$	$1217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−0.352093	−	0.609843i	−0.157461	−	0.272730i	0.776491	−	0.630128i	$-0.216997\pi$
$5$	−0.352093	−	0.609843i	−0.157461	−	0.272730i	−0.933952	+	0.357397i	$0.883664\pi$
$6$		0			0
$7$		−	0.0726253i		−	0.0274498i	−0.999906	−	0.0137249i	$-0.995631\pi$
$7$		−	0.0726253i		−	0.0274498i	0.999906	−	0.0137249i	$-0.00436890\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$		−	1.77299i		−	0.534576i	−0.963617	−	0.267288i	$-0.913872\pi$
$11$		−	1.77299i		−	0.534576i	0.963617	−	0.267288i	$-0.0861276\pi$
$12$		0			0
$13$	2.42846	+	1.40207i	0.673532	+	0.388864i	0.797414	−	0.603433i	$-0.206201\pi$
$13$	2.42846	+	1.40207i	0.673532	+	0.388864i	−0.123881	+	0.992297i	$0.539534\pi$
$14$		0			0
$15$	−0.352093	+	0.609843i	−0.0909101	+	0.157461i
$16$		0			0
$17$	3.41547	+	5.91577i	0.828374	+	1.43479i	0.899313	+	0.437305i	$0.144067\pi$
$17$	3.41547	+	5.91577i	0.828374	+	1.43479i	−0.0709391	+	0.997481i	$0.522600\pi$
$18$		0			0
$19$	−3.54782	+	2.53239i	−0.813925	+	0.580970i
$19$	−3.54782	+	2.53239i	−0.813925	+	0.580970i
$20$		0			0
$21$	−0.0628953	+	0.0363126i	−0.0137249	+	0.00792407i
$22$		0			0
$23$	4.39446	+	2.53714i	0.916309	+	0.529031i	0.882456	−	0.470396i	$-0.155889\pi$
$23$	4.39446	+	2.53714i	0.916309	+	0.529031i	0.0338530	+	0.999427i	$0.489222\pi$
$24$		0			0
$25$	2.25206	−	3.90068i	0.450412	−	0.780137i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−5.17824	−	2.98966i	−0.961575	−	0.555166i	−0.0649175	−	0.997891i	$-0.520678\pi$
$29$	−5.17824	−	2.98966i	−0.961575	−	0.555166i	−0.896657	+	0.442725i	$0.854012\pi$
$30$		0			0
$31$	0.690868			0.124083			0.0620417	−	0.998074i	$-0.480239\pi$
$31$	0.690868			0.124083			0.0620417	+	0.998074i	$0.480239\pi$
$32$		0			0
$33$	−1.53545	+	0.886495i	−0.267288	+	0.154319i
$34$		0			0
$35$	−0.0442900	+	0.0255709i	−0.00748638	+	0.00432227i
$36$		0			0
$37$			10.7779i			1.77188i	0.463797	+	0.885941i	$0.346487\pi$
$37$			10.7779i			1.77188i	−0.463797	+	0.885941i	$0.653513\pi$
$38$		0			0
$39$		−	2.80414i		−	0.449022i
$40$		0			0
$41$	−1.04119	+	0.601130i	−0.162606	+	0.0938808i	−0.579095	−	0.815260i	$-0.696594\pi$
$41$	−1.04119	+	0.601130i	−0.162606	+	0.0938808i	0.416489	+	0.909141i	$0.363261\pi$
$42$		0			0
$43$	9.49783	−	5.48357i	1.44841	−	0.836237i	0.450019	−	0.893019i	$-0.351417\pi$
$43$	9.49783	−	5.48357i	1.44841	−	0.836237i	0.998387	+	0.0567821i	$0.0180840\pi$
$44$		0			0
$45$	0.704186			0.104974
$46$		0			0
$47$	−3.35724	−	1.93830i	−0.489704	−	0.282731i	0.234748	−	0.972056i	$-0.424574\pi$
$47$	−3.35724	−	1.93830i	−0.489704	−	0.282731i	−0.724451	+	0.689326i	$0.757907\pi$
$48$		0			0
$49$	6.99473			0.999247
$50$		0			0
$51$	3.41547	−	5.91577i	0.478262	−	0.828374i
$52$		0			0
$53$	9.05207	+	5.22621i	1.24340	+	0.717876i	0.969784	−	0.243964i	$-0.0784480\pi$
$53$	9.05207	+	5.22621i	1.24340	+	0.717876i	0.273613	+	0.961840i	$0.411781\pi$
$54$		0			0
$55$	−1.08125	+	0.624257i	−0.145795	+	0.0841749i
$56$		0			0
$57$	3.96702	+	1.80630i	0.525445	+	0.239251i
$58$		0			0
$59$	−7.24248	−	12.5443i	−0.942890	−	1.63313i	−0.759921	−	0.650015i	$-0.774762\pi$
$59$	−7.24248	−	12.5443i	−0.942890	−	1.63313i	−0.182969	−	0.983119i	$-0.558571\pi$
$60$		0			0
$61$	4.69049	−	8.12417i	0.600556	−	1.04019i	−0.392181	−	0.919888i	$-0.628279\pi$
$61$	4.69049	−	8.12417i	0.600556	−	1.04019i	0.992737	−	0.120305i	$-0.0383873\pi$
$62$		0			0
$63$	0.0628953	+	0.0363126i	0.00792407	+	0.00457496i
$64$		0			0
$65$		−	1.97464i		−	0.244924i
$66$		0			0
$67$	1.61637	−	2.79963i	0.197471	−	0.342029i	−0.750237	−	0.661169i	$-0.770061\pi$
$67$	1.61637	−	2.79963i	0.197471	−	0.342029i	0.947708	+	0.319140i	$0.103394\pi$
$68$		0			0
$69$		−	5.07429i		−	0.610872i
$70$		0			0
$71$	−1.90279	−	3.29573i	−0.225820	−	0.391131i	0.730745	−	0.682650i	$-0.239173\pi$
$71$	−1.90279	−	3.29573i	−0.225820	−	0.391131i	−0.956565	+	0.291519i	$0.905839\pi$
$72$		0			0
$73$	5.46110	+	9.45890i	0.639173	+	1.10708i	0.985614	+	0.169009i	$0.0540567\pi$
$73$	5.46110	+	9.45890i	0.639173	+	1.10708i	−0.346441	+	0.938072i	$0.612610\pi$
$74$		0			0
$75$	−4.50412			−0.520091
$76$		0			0
$77$	−0.128764			−0.0146740
$78$		0			0
$79$	5.68613	+	9.84867i	0.639740	+	1.10806i	0.985490	+	0.169735i	$0.0542913\pi$
$79$	5.68613	+	9.84867i	0.639740	+	1.10806i	−0.345750	+	0.938327i	$0.612375\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	11.2982i		−	1.24014i	−0.784547	−	0.620070i	$-0.787104\pi$
$83$		−	11.2982i		−	1.24014i	0.784547	−	0.620070i	$-0.212896\pi$
$84$		0			0
$85$	2.40513	−	4.16581i	0.260873	−	0.451845i
$86$		0			0
$87$			5.97932i			0.641050i
$88$		0			0
$89$	7.06701	+	4.08014i	0.749102	+	0.432494i	0.825369	−	0.564593i	$-0.190967\pi$
$89$	7.06701	+	4.08014i	0.749102	+	0.432494i	−0.0762674	+	0.997087i	$0.524300\pi$
$90$		0			0
$91$	0.101826	−	0.176367i	0.0106742	−	0.0184883i
$92$		0			0
$93$	−0.345434	−	0.598309i	−0.0358198	−	0.0620417i
$94$		0			0
$95$	2.79352	+	1.27197i	0.286609	+	0.130502i
$96$		0			0
$97$	−6.90853	+	3.98864i	−0.701455	+	0.404985i	−0.807889	−	0.589334i	$-0.799390\pi$
$97$	−6.90853	+	3.98864i	−0.701455	+	0.404985i	0.106434	+	0.994320i	$0.466057\pi$
$98$		0			0
$99$	1.53545	+	0.886495i	0.154319	+	0.0890961i
$100$		0			0
$101$	−7.57609	+	13.1222i	−0.753850	+	1.30571i	0.192095	+	0.981376i	$0.438472\pi$
$101$	−7.57609	+	13.1222i	−0.753850	+	1.30571i	−0.945944	+	0.324329i	$0.894861\pi$
$102$		0			0
$103$	5.50018			0.541949			0.270975	−	0.962587i	$-0.412654\pi$
$103$	5.50018			0.541949			0.270975	+	0.962587i	$0.412654\pi$
$104$		0			0
$105$	0.0442900	+	0.0255709i	0.00432227	+	0.00249546i
$106$		0			0
$107$	11.3724			1.09941			0.549706	−	0.835358i	$-0.314740\pi$
$107$	11.3724			1.09941			0.549706	+	0.835358i	$0.314740\pi$
$108$		0			0
$109$	13.3765	−	7.72294i	1.28124	−	0.739724i	0.304164	−	0.952620i	$-0.401623\pi$
$109$	13.3765	−	7.72294i	1.28124	−	0.739724i	0.977075	+	0.212896i	$0.0682896\pi$
$110$		0			0
$111$	9.33397	−	5.38897i	0.885941	−	0.511499i
$112$		0			0
$113$		−	4.06196i		−	0.382117i	−0.981579	−	0.191058i	$-0.938808\pi$
$113$		−	4.06196i		−	0.382117i	0.981579	−	0.191058i	$-0.0611920\pi$
$114$		0			0
$115$		−	3.57324i		−	0.333207i
$116$		0			0
$117$	−2.42846	+	1.40207i	−0.224511	+	0.129621i
$118$		0			0
$119$	0.429635	−	0.248050i	0.0393846	−	0.0227387i
$120$		0			0
$121$	7.85651			0.714228
$122$		0			0
$123$	1.04119	+	0.601130i	0.0938808	+	0.0542021i
$124$		0			0
$125$	−6.69267			−0.598611
$126$		0			0
$127$	−6.27231	+	10.8640i	−0.556577	+	0.964020i	0.441202	+	0.897408i	$0.354552\pi$
$127$	−6.27231	+	10.8640i	−0.556577	+	0.964020i	−0.997779	+	0.0666120i	$0.978781\pi$
$128$		0			0
$129$	−9.49783	−	5.48357i	−0.836237	−	0.482802i
$130$		0			0
$131$	12.6088	−	7.27968i	1.10163	−	0.636029i	0.164985	−	0.986296i	$-0.447243\pi$
$131$	12.6088	−	7.27968i	1.10163	−	0.636029i	0.936650	+	0.350267i	$0.113909\pi$
$132$		0			0
$133$	0.183916	+	0.257661i	0.0159475	+	0.0223421i
$134$		0			0
$135$	−0.352093	−	0.609843i	−0.0303034	−	0.0524870i
$136$		0			0
$137$	7.12304	−	12.3375i	0.608562	−	1.05406i	−0.382915	−	0.923783i	$-0.625080\pi$
$137$	7.12304	−	12.3375i	0.608562	−	1.05406i	0.991478	−	0.130277i	$-0.0415868\pi$
$138$		0			0
$139$	−12.2017	−	7.04467i	−1.03494	−	0.597521i	−0.116541	−	0.993186i	$-0.537181\pi$
$139$	−12.2017	−	7.04467i	−1.03494	−	0.597521i	−0.918395	+	0.395665i	$0.870514\pi$
$140$		0			0
$141$			3.87661i			0.326469i
$142$		0			0
$143$	2.48585	−	4.30562i	0.207878	−	0.360054i
$144$		0			0
$145$			4.21055i			0.349667i
$146$		0			0
$147$	−3.49736	−	6.05761i	−0.288458	−	0.499623i
$148$		0			0
$149$	−3.73874	−	6.47569i	−0.306290	−	0.530509i	0.671258	−	0.741224i	$-0.265754\pi$
$149$	−3.73874	−	6.47569i	−0.306290	−	0.530509i	−0.977548	+	0.210714i	$0.932421\pi$
$150$		0			0
$151$	−10.0151			−0.815015			−0.407508	−	0.913202i	$-0.633602\pi$
$151$	−10.0151			−0.815015			−0.407508	+	0.913202i	$0.633602\pi$
$152$		0			0
$153$	−6.83095			−0.552249
$154$		0			0
$155$	−0.243250	−	0.421321i	−0.0195383	−	0.0338413i
$156$		0			0
$157$	5.02195	+	8.69827i	0.400795	+	0.694197i	0.993822	−	0.110985i	$-0.0354006\pi$
$157$	5.02195	+	8.69827i	0.400795	+	0.694197i	−0.593027	+	0.805183i	$0.702067\pi$
$158$		0			0
$159$		−	10.4524i		−	0.828931i
$160$		0			0
$161$	0.184261	−	0.319149i	0.0145218	−	0.0251525i
$162$		0			0
$163$			0.808933i			0.0633605i	0.999498	+	0.0316802i	$0.0100858\pi$
$163$			0.808933i			0.0633605i	−0.999498	+	0.0316802i	$0.989914\pi$
$164$		0			0
$165$	1.08125	+	0.624257i	0.0841749	+	0.0485984i
$166$		0			0
$167$	3.82191	−	6.61974i	0.295748	−	0.512251i	−0.679410	−	0.733759i	$-0.737764\pi$
$167$	3.82191	−	6.61974i	0.295748	−	0.512251i	0.975159	+	0.221507i	$0.0710977\pi$
$168$		0			0
$169$	−2.56840	−	4.44861i	−0.197569	−	0.342200i
$170$		0			0
$171$	−0.419206	−	4.33869i	−0.0320575	−	0.331788i
$172$		0			0
$173$	9.84543	−	5.68426i	0.748534	−	0.432166i	−0.0766300	−	0.997060i	$-0.524416\pi$
$173$	9.84543	−	5.68426i	0.748534	−	0.432166i	0.825164	+	0.564893i	$0.191083\pi$
$174$		0			0
$175$	−0.283288	−	0.163557i	−0.0214146	−	0.0123637i
$176$		0			0
$177$	−7.24248	+	12.5443i	−0.544378	+	0.942890i
$178$		0			0
$179$	4.75125			0.355125			0.177562	−	0.984110i	$-0.443179\pi$
$179$	4.75125			0.355125			0.177562	+	0.984110i	$0.443179\pi$
$180$		0			0
$181$	1.06823	+	0.616745i	0.0794011	+	0.0458423i	0.539175	−	0.842194i	$-0.318736\pi$
$181$	1.06823	+	0.616745i	0.0794011	+	0.0458423i	−0.459774	+	0.888036i	$0.652070\pi$
$182$		0			0
$183$	−9.38098			−0.693462
$184$		0			0
$185$	6.57286	−	3.79484i	0.483246	−	0.279002i
$186$		0			0
$187$	10.4886	−	6.05560i	0.767003	−	0.442829i
$188$		0			0
$189$		−	0.0726253i		−	0.00528271i
$190$		0			0
$191$			20.1291i			1.45649i	0.685316	+	0.728246i	$0.259664\pi$
$191$			20.1291i			1.45649i	−0.685316	+	0.728246i	$0.740336\pi$
$192$		0			0
$193$	8.89392	−	5.13491i	0.640198	−	0.369619i	−0.144493	−	0.989506i	$-0.546155\pi$
$193$	8.89392	−	5.13491i	0.640198	−	0.369619i	0.784691	+	0.619887i	$0.212822\pi$
$194$		0			0
$195$	−1.71009	+	0.987318i	−0.122462	+	0.0707033i
$196$		0			0
$197$	−27.6742			−1.97170			−0.985852	−	0.167621i	$-0.946392\pi$
$197$	−27.6742			−1.97170			−0.985852	+	0.167621i	$0.946392\pi$
$198$		0			0
$199$	17.0440	+	9.84037i	1.20822	+	0.697566i	0.962370	−	0.271742i	$-0.0875999\pi$
$199$	17.0440	+	9.84037i	1.20822	+	0.697566i	0.245849	+	0.969308i	$0.420933\pi$
$200$		0			0
$201$	−3.23274			−0.228020
$202$		0			0
$203$	−0.217125	+	0.376071i	−0.0152392	+	0.0263950i
$204$		0			0
$205$	0.733190	+	0.423308i	0.0512082	+	0.0295651i
$206$		0			0
$207$	−4.39446	+	2.53714i	−0.305436	+	0.176344i
$208$		0			0
$209$	4.48990	+	6.29024i	0.310573	+	0.435105i
$210$		0			0
$211$	9.80726	+	16.9867i	0.675160	+	1.16941i	0.976422	+	0.215870i	$0.0692586\pi$
$211$	9.80726	+	16.9867i	0.675160	+	1.16941i	−0.301262	+	0.953541i	$0.597408\pi$
$212$		0			0
$213$	−1.90279	+	3.29573i	−0.130377	+	0.225820i
$214$		0			0
$215$	−6.68824	−	3.86146i	−0.456134	−	0.263349i
$216$		0			0
$217$		−	0.0501745i		−	0.00340606i
$218$		0			0
$219$	5.46110	−	9.45890i	0.369027	−	0.639173i
$220$		0			0
$221$			19.1549i			1.28850i
$222$		0			0
$223$	11.7774	+	20.3991i	0.788675	+	1.36603i	0.926779	+	0.375608i	$0.122566\pi$
$223$	11.7774	+	20.3991i	0.788675	+	1.36603i	−0.138103	+	0.990418i	$0.544101\pi$
$224$		0			0
$225$	2.25206	+	3.90068i	0.150137	+	0.260046i
$226$		0			0
$227$	−2.92483			−0.194128			−0.0970639	−	0.995278i	$-0.530945\pi$
$227$	−2.92483			−0.194128			−0.0970639	+	0.995278i	$0.530945\pi$
$228$		0			0
$229$	17.3383			1.14574			0.572872	−	0.819645i	$-0.305829\pi$
$229$	17.3383			1.14574			0.572872	+	0.819645i	$0.305829\pi$
$230$		0			0
$231$	0.0643819	+	0.111513i	0.00423602	+	0.00733700i
$232$		0			0
$233$	−5.27035	−	9.12851i	−0.345272	−	0.598029i	0.640131	−	0.768266i	$-0.278880\pi$
$233$	−5.27035	−	9.12851i	−0.345272	−	0.598029i	−0.985403	+	0.170237i	$0.945547\pi$
$234$		0			0
$235$			2.72985i			0.178076i
$236$		0			0
$237$	5.68613	−	9.84867i	0.369354	−	0.639740i
$238$		0			0
$239$			4.23256i			0.273782i	0.990586	+	0.136891i	$0.0437110\pi$
$239$			4.23256i			0.273782i	−0.990586	+	0.136891i	$0.956289\pi$
$240$		0			0
$241$	−0.304695	−	0.175916i	−0.0196271	−	0.0113317i	0.490154	−	0.871636i	$-0.336940\pi$
$241$	−0.304695	−	0.175916i	−0.0196271	−	0.0113317i	−0.509781	+	0.860304i	$0.670274\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−2.46280	−	4.26569i	−0.157342	−	0.272525i
$246$		0			0
$247$	−12.1663	+	1.17551i	−0.774123	+	0.0747961i
$248$		0			0
$249$	−9.78453	+	5.64910i	−0.620070	+	0.357997i
$250$		0			0
$251$	−21.1101	−	12.1879i	−1.33246	−	0.769294i	−0.346781	−	0.937946i	$-0.612725\pi$
$251$	−21.1101	−	12.1879i	−1.33246	−	0.769294i	−0.985676	+	0.168652i	$0.946059\pi$
$252$		0			0
$253$	4.49833	−	7.79133i	0.282807	−	0.489837i
$254$		0			0
$255$	−4.81026			−0.301230
$256$		0			0
$257$	−16.5851	−	9.57542i	−1.03455	−	0.597298i	−0.116266	−	0.993218i	$-0.537093\pi$
$257$	−16.5851	−	9.57542i	−1.03455	−	0.597298i	−0.918285	+	0.395920i	$0.870426\pi$
$258$		0			0
$259$	0.782751			0.0486378
$260$		0			0
$261$	5.17824	−	2.98966i	0.320525	−	0.185055i
$262$		0			0
$263$	−2.68676	+	1.55120i	−0.165673	+	0.0956511i	−0.580544	−	0.814229i	$-0.697160\pi$
$263$	−2.68676	+	1.55120i	−0.165673	+	0.0956511i	0.414871	+	0.909880i	$0.363827\pi$
$264$		0			0
$265$		−	7.36046i		−	0.452149i
$266$		0			0
$267$		−	8.16028i		−	0.499401i
$268$		0			0
$269$	−10.4435	+	6.02956i	−0.636752	+	0.367629i	−0.783362	−	0.621566i	$-0.786497\pi$
$269$	−10.4435	+	6.02956i	−0.636752	+	0.367629i	0.146611	+	0.989194i	$0.453164\pi$
$270$		0			0
$271$	−7.43530	+	4.29277i	−0.451662	+	0.260767i	−0.708532	−	0.705679i	$-0.750642\pi$
$271$	−7.43530	+	4.29277i	−0.451662	+	0.260767i	0.256870	+	0.966446i	$0.417309\pi$
$272$		0			0
$273$	−0.203651			−0.0123255
$274$		0			0
$275$	−6.91587	−	3.99288i	−0.417043	−	0.240780i
$276$		0			0
$277$	7.50557			0.450966			0.225483	−	0.974247i	$-0.427604\pi$
$277$	7.50557			0.450966			0.225483	+	0.974247i	$0.427604\pi$
$278$		0			0
$279$	−0.345434	+	0.598309i	−0.0206806	+	0.0358198i
$280$		0			0
$281$	−1.65380	−	0.954820i	−0.0986572	−	0.0569598i	0.449860	−	0.893099i	$-0.351474\pi$
$281$	−1.65380	−	0.954820i	−0.0986572	−	0.0569598i	−0.548517	+	0.836140i	$0.684807\pi$
$282$		0			0
$283$	−23.5620	+	13.6035i	−1.40061	+	0.808644i	−0.994455	−	0.105159i	$-0.966465\pi$
$283$	−23.5620	+	13.6035i	−1.40061	+	0.808644i	−0.406158	+	0.913803i	$0.633132\pi$
$284$		0			0
$285$	−0.295199	−	3.05525i	−0.0174861	−	0.180977i
$286$		0			0
$287$	0.0436572	+	0.0756166i	0.00257701	+	0.00446351i
$288$		0			0
$289$	−14.8309	+	25.6879i	−0.872407	+	1.51105i
$290$		0			0
$291$	6.90853	+	3.98864i	0.404985	+	0.233818i
$292$		0			0
$293$			11.0983i			0.648372i	0.945993	+	0.324186i	$0.105090\pi$
$293$			11.0983i			0.648372i	−0.945993	+	0.324186i	$0.894910\pi$
$294$		0			0
$295$	−5.10005	+	8.83355i	−0.296937	+	0.514309i
$296$		0			0
$297$		−	1.77299i		−	0.102879i
$298$		0			0
$299$	7.11450	+	12.3227i	0.411442	+	0.712639i
$300$		0			0
$301$	−0.398246	−	0.689782i	−0.0229545	−	0.0397584i
$302$		0			0
$303$	15.1522			0.870471
$304$		0			0
$305$	−6.60596			−0.378256
$306$		0			0
$307$	3.95490	+	6.85009i	0.225718	+	0.390955i	0.956535	−	0.291619i	$-0.0941938\pi$
$307$	3.95490	+	6.85009i	0.225718	+	0.390955i	−0.730816	+	0.682574i	$0.760860\pi$
$308$		0			0
$309$	−2.75009	−	4.76330i	−0.156447	−	0.270975i
$310$		0			0
$311$			21.0104i			1.19139i	0.803211	+	0.595694i	$0.203123\pi$
$311$			21.0104i			1.19139i	−0.803211	+	0.595694i	$0.796877\pi$
$312$		0			0
$313$	3.84777	−	6.66453i	0.217489	−	0.376702i	−0.736551	−	0.676382i	$-0.763547\pi$
$313$	3.84777	−	6.66453i	0.217489	−	0.376702i	0.954040	+	0.299681i	$0.0968801\pi$
$314$		0			0
$315$		−	0.0511417i		−	0.00288151i
$316$		0			0
$317$	−15.5232	−	8.96234i	−0.871872	−	0.503375i	−0.00390184	−	0.999992i	$-0.501242\pi$
$317$	−15.5232	−	8.96234i	−0.871872	−	0.503375i	−0.867970	+	0.496617i	$0.834575\pi$
$318$		0			0
$319$	−5.30063	+	9.18096i	−0.296778	+	0.514035i
$320$		0			0
$321$	−5.68621	−	9.84880i	−0.317373	−	0.549706i
$322$		0			0
$323$	−27.0985	−	12.3388i	−1.50780	−	0.686547i
$324$		0			0
$325$	10.9381	−	6.31509i	0.606734	−	0.350298i
$326$		0			0
$327$	−13.3765	−	7.72294i	−0.739724	−	0.427080i
$328$		0			0
$329$	−0.140770	+	0.243820i	−0.00776089	+	0.0134423i
$330$		0			0
$331$	−25.3504			−1.39338			−0.696692	−	0.717371i	$-0.745345\pi$
$331$	−25.3504			−1.39338			−0.696692	+	0.717371i	$0.745345\pi$
$332$		0			0
$333$	−9.33397	−	5.38897i	−0.511499	−	0.295314i
$334$		0			0
$335$	−2.27645			−0.124376
$336$		0			0
$337$	−8.04964	+	4.64746i	−0.438492	+	0.253163i	−0.702958	−	0.711232i	$-0.748138\pi$
$337$	−8.04964	+	4.64746i	−0.438492	+	0.253163i	0.264466	+	0.964395i	$0.414804\pi$
$338$		0			0
$339$	−3.51776	+	2.03098i	−0.191058	+	0.110308i
$340$		0			0
$341$		−	1.22490i		−	0.0663321i
$342$		0			0
$343$		−	1.01637i		−	0.0548789i
$344$		0			0
$345$	−3.09452	+	1.78662i	−0.166603	+	0.0961885i
$346$		0			0
$347$	8.44926	−	4.87818i	0.453580	−	0.261875i	−0.255761	−	0.966740i	$-0.582326\pi$
$347$	8.44926	−	4.87818i	0.453580	−	0.261875i	0.709341	+	0.704865i	$0.248993\pi$
$348$		0			0
$349$	15.0537			0.805808			0.402904	−	0.915242i	$-0.368001\pi$
$349$	15.0537			0.805808			0.402904	+	0.915242i	$0.368001\pi$
$350$		0			0
$351$	2.42846	+	1.40207i	0.129621	+	0.0748369i
$352$		0			0
$353$	13.6139			0.724593			0.362297	−	0.932063i	$-0.381993\pi$
$353$	13.6139			0.724593			0.362297	+	0.932063i	$0.381993\pi$
$354$		0			0
$355$	−1.33992	+	2.32081i	−0.0711155	+	0.123176i
$356$		0			0
$357$	−0.429635	−	0.248050i	−0.0227387	−	0.0131282i
$358$		0			0
$359$	7.35127	−	4.24426i	0.387985	−	0.224003i	−0.293301	−	0.956020i	$-0.594754\pi$
$359$	7.35127	−	4.24426i	0.387985	−	0.224003i	0.681287	+	0.732017i	$0.261421\pi$
$360$		0			0
$361$	6.17400	−	17.9689i	0.324947	−	0.945732i
$362$		0			0
$363$	−3.92825	−	6.80394i	−0.206180	−	0.357114i
$364$		0			0
$365$	3.84563	−	6.66083i	0.201290	−	0.348644i
$366$		0			0
$367$	8.04723	+	4.64607i	0.420062	+	0.242523i	0.695104	−	0.718909i	$-0.255358\pi$
$367$	8.04723	+	4.64607i	0.420062	+	0.242523i	−0.275042	+	0.961432i	$0.588692\pi$
$368$		0			0
$369$		−	1.20226i		−	0.0625872i
$370$		0			0
$371$	0.379555	−	0.657409i	0.0197055	−	0.0341310i
$372$		0			0
$373$			22.2938i			1.15433i	0.816628	+	0.577165i	$0.195841\pi$
$373$			22.2938i			1.15433i	−0.816628	+	0.577165i	$0.804159\pi$
$374$		0			0
$375$	3.34634	+	5.79603i	0.172804	+	0.299305i
$376$		0			0
$377$	−8.38342	−	14.5205i	−0.431768	−	0.747844i
$378$		0			0
$379$	15.9462			0.819100			0.409550	−	0.912288i	$-0.365686\pi$
$379$	15.9462			0.819100			0.409550	+	0.912288i	$0.365686\pi$
$380$		0			0
$381$	12.5446			0.642680
$382$		0			0
$383$	−12.7623	−	22.1050i	−0.652125	−	1.12951i	−0.982606	−	0.185701i	$-0.940544\pi$
$383$	−12.7623	−	22.1050i	−0.652125	−	1.12951i	0.330481	−	0.943813i	$-0.392789\pi$
$384$		0			0
$385$	0.0453369	+	0.0785258i	0.00231058	+	0.00400204i
$386$		0			0
$387$			10.9671i			0.557491i
$388$		0			0
$389$	−11.4743	+	19.8741i	−0.581770	+	1.00765i	0.413500	+	0.910504i	$0.364306\pi$
$389$	−11.4743	+	19.8741i	−0.581770	+	1.00765i	−0.995270	+	0.0971507i	$0.969027\pi$
$390$		0			0
$391$			34.6622i			1.75294i
$392$		0			0
$393$	−12.6088	−	7.27968i	−0.636029	−	0.367211i
$394$		0			0
$395$	4.00410	−	6.93530i	0.201468	−	0.348953i
$396$		0			0
$397$	−10.5592	−	18.2891i	−0.529953	−	0.917906i	−0.999389	−	0.0349393i	$-0.988876\pi$
$397$	−10.5592	−	18.2891i	−0.529953	−	0.917906i	0.469436	−	0.882966i	$-0.344457\pi$
$398$		0			0
$399$	0.131183	−	0.288106i	0.00656738	−	0.0144233i
$400$		0			0
$401$	3.66180	−	2.11414i	0.182862	−	0.105575i	−0.405775	−	0.913973i	$-0.632998\pi$
$401$	3.66180	−	2.11414i	0.182862	−	0.105575i	0.588636	+	0.808398i	$0.299665\pi$
$402$		0			0
$403$	1.67774	+	0.968644i	0.0835742	+	0.0482516i
$404$		0			0
$405$	−0.352093	+	0.609843i	−0.0174957	+	0.0303034i
$406$		0			0
$407$	19.1092			0.947207
$408$		0			0
$409$	−33.2638	−	19.2049i	−1.64479	−	0.949621i	−0.979096	−	0.203397i	$-0.934802\pi$
$409$	−33.2638	−	19.2049i	−1.64479	−	0.949621i	−0.665695	−	0.746224i	$-0.731865\pi$
$410$		0			0
$411$	−14.2461			−0.702707
$412$		0			0
$413$	−0.911036	+	0.525987i	−0.0448292	+	0.0258821i
$414$		0			0
$415$	−6.89014	+	3.97802i	−0.338223	+	0.195273i
$416$		0			0
$417$			14.0893i			0.689957i
$418$		0			0
$419$			29.1398i			1.42357i	0.702397	+	0.711786i	$0.252113\pi$
$419$			29.1398i			1.42357i	−0.702397	+	0.711786i	$0.747887\pi$
$420$		0			0
$421$	−21.2601	+	12.2745i	−1.03615	+	0.598224i	−0.918742	−	0.394859i	$-0.870793\pi$
$421$	−21.2601	+	12.2745i	−1.03615	+	0.598224i	−0.117413	+	0.993083i	$0.537460\pi$
$422$		0			0
$423$	3.35724	−	1.93830i	0.163235	−	0.0942435i
$424$		0			0
$425$	30.7674			1.49244
$426$		0			0
$427$	−0.590020	−	0.340648i	−0.0285531	−	0.0164851i
$428$		0			0
$429$	−4.97171			−0.240036
$430$		0			0
$431$	−13.4042	+	23.2168i	−0.645658	+	1.11831i	0.338492	+	0.940969i	$0.390083\pi$
$431$	−13.4042	+	23.2168i	−0.645658	+	1.11831i	−0.984149	+	0.177342i	$0.943250\pi$
$432$		0			0
$433$	−1.13851	−	0.657320i	−0.0547133	−	0.0315888i	0.472394	−	0.881388i	$-0.343390\pi$
$433$	−1.13851	−	0.657320i	−0.0547133	−	0.0315888i	−0.527107	+	0.849799i	$0.676723\pi$
$434$		0			0
$435$	3.64645	−	2.10528i	0.174834	−	0.100940i
$436$		0			0
$437$	−22.0158	+	2.12717i	−1.05316	+	0.101756i
$438$		0			0
$439$	−17.2505	−	29.8787i	−0.823321	−	1.42603i	−0.903196	−	0.429229i	$-0.858785\pi$
$439$	−17.2505	−	29.8787i	−0.823321	−	1.42603i	0.0798742	−	0.996805i	$-0.474548\pi$
$440$		0			0
$441$	−3.49736	+	6.05761i	−0.166541	+	0.288458i
$442$		0			0
$443$	23.2827	+	13.4423i	1.10620	+	0.638663i	0.937842	−	0.347064i	$-0.112821\pi$
$443$	23.2827	+	13.4423i	1.10620	+	0.638663i	0.168355	+	0.985726i	$0.446155\pi$
$444$		0			0
$445$		−	5.74636i		−	0.272404i
$446$		0			0
$447$	−3.73874	+	6.47569i	−0.176836	+	0.306290i
$448$		0			0
$449$			15.3531i			0.724560i	0.932069	+	0.362280i	$0.118002\pi$
$449$			15.3531i			0.724560i	−0.932069	+	0.362280i	$0.881998\pi$
$450$		0			0
$451$	1.06580	+	1.84601i	0.0501864	+	0.0869254i
$452$		0			0
$453$	5.00754	+	8.67331i	0.235275	+	0.407508i
$454$		0			0
$455$	−0.143409			−0.00672310
$456$		0			0
$457$	26.1671			1.22404			0.612022	−	0.790841i	$-0.290356\pi$
$457$	26.1671			1.22404			0.612022	+	0.790841i	$0.290356\pi$
$458$		0			0
$459$	3.41547	+	5.91577i	0.159421	+	0.276125i
$460$		0			0
$461$	−19.4541	−	33.6956i	−0.906069	−	1.56936i	−0.819475	−	0.573115i	$-0.805735\pi$
$461$	−19.4541	−	33.6956i	−0.906069	−	1.56936i	−0.0865942	−	0.996244i	$-0.527598\pi$
$462$		0			0
$463$		−	10.4149i		−	0.484019i	−0.970274	−	0.242010i	$-0.922193\pi$
$463$		−	10.4149i		−	0.484019i	0.970274	−	0.242010i	$-0.0778066\pi$
$464$		0			0
$465$	−0.243250	+	0.421321i	−0.0112804	+	0.0195383i
$466$		0			0
$467$			30.0215i			1.38923i	0.719382	+	0.694615i	$0.244425\pi$
$467$			30.0215i			1.38923i	−0.719382	+	0.694615i	$0.755575\pi$
$468$		0			0
$469$	−0.203324	−	0.117389i	−0.00938863	−	0.00542053i
$470$		0			0
$471$	5.02195	−	8.69827i	0.231399	−	0.400795i
$472$		0			0
$473$	−9.72232	−	16.8395i	−0.447033	−	0.774283i
$474$		0			0
$475$	1.88816	+	19.5420i	0.0866345	+	0.896649i
$476$		0			0
$477$	−9.05207	+	5.22621i	−0.414466	+	0.239292i
$478$		0			0
$479$	−26.7708	−	15.4561i	−1.22319	−	0.706208i	−0.257592	−	0.966254i	$-0.582929\pi$
$479$	−26.7708	−	15.4561i	−1.22319	−	0.706208i	−0.965596	+	0.260046i	$0.916262\pi$
$480$		0			0
$481$	−15.1114	+	26.1738i	−0.689022	+	1.19342i
$482$		0			0
$483$	−0.368522			−0.0167683
$484$		0			0
$485$	4.86490	+	2.80875i	0.220904	+	0.127539i
$486$		0			0
$487$	−19.4901			−0.883181			−0.441591	−	0.897217i	$-0.645586\pi$
$487$	−19.4901			−0.883181			−0.441591	+	0.897217i	$0.645586\pi$
$488$		0			0
$489$	0.700556	−	0.404466i	0.0316802	−	0.0182906i
$490$		0			0
$491$	5.47165	−	3.15906i	0.246932	−	0.142566i	−0.371427	−	0.928462i	$-0.621131\pi$
$491$	5.47165	−	3.15906i	0.246932	−	0.142566i	0.618359	+	0.785896i	$0.287798\pi$
$492$		0			0
$493$		−	40.8444i		−	1.83954i
$494$		0			0
$495$		−	1.24851i		−	0.0561166i
$496$		0			0
$497$	−0.239353	+	0.138191i	−0.0107365	+	0.00619870i
$498$		0			0
$499$	7.98695	−	4.61127i	0.357545	−	0.206429i	−0.310458	−	0.950587i	$-0.600482\pi$
$499$	7.98695	−	4.61127i	0.357545	−	0.206429i	0.668003	+	0.744158i	$0.267149\pi$
$500$		0			0
$501$	−7.64382			−0.341501
$502$		0			0
$503$	−5.95331	−	3.43715i	−0.265445	−	0.153255i	0.361371	−	0.932422i	$-0.382309\pi$
$503$	−5.95331	−	3.43715i	−0.265445	−	0.153255i	−0.626816	+	0.779167i	$0.715642\pi$
$504$		0			0
$505$	10.6700			0.474807
$506$		0			0
$507$	−2.56840	+	4.44861i	−0.114067	+	0.197569i
$508$		0			0
$509$	6.78994	+	3.92017i	0.300959	+	0.173759i	0.642874	−	0.765972i	$-0.277742\pi$
$509$	6.78994	+	3.92017i	0.300959	+	0.173759i	−0.341915	+	0.939731i	$0.611075\pi$
$510$		0			0
$511$	0.686955	−	0.396614i	0.0303891	−	0.0175452i
$512$		0			0
$513$	−3.54782	+	2.53239i	−0.156640	+	0.111808i
$514$		0			0
$515$	−1.93658	−	3.35425i	−0.0853358	−	0.147806i
$516$		0			0
$517$	−3.43659	+	5.95235i	−0.151141	+	0.261784i
$518$		0			0
$519$	−9.84543	−	5.68426i	−0.432166	−	0.249511i
$520$		0			0
$521$			4.93216i			0.216082i	0.994146	+	0.108041i	$0.0344578\pi$
$521$			4.93216i			0.216082i	−0.994146	+	0.108041i	$0.965542\pi$
$522$		0			0
$523$	−2.81281	+	4.87194i	−0.122996	+	0.213035i	−0.920948	−	0.389686i	$-0.872583\pi$
$523$	−2.81281	+	4.87194i	−0.122996	+	0.213035i	0.797952	+	0.602721i	$0.205917\pi$
$524$		0			0
$525$			0.327113i			0.0142764i
$526$		0			0
$527$	2.35964	+	4.08702i	0.102788	+	0.178033i
$528$		0			0
$529$	1.37419	+	2.38017i	0.0597475	+	0.103486i
$530$		0			0
$531$	14.4850			0.628594
$532$		0			0
$533$	−3.37130			−0.146027
$534$		0			0
$535$	−4.00415	−	6.93539i	−0.173114	−	0.299843i
$536$		0			0
$537$	−2.37562	−	4.11470i	−0.102516	−	0.177562i
$538$		0			0
$539$		−	12.4016i		−	0.534174i
$540$		0			0
$541$	3.88423	−	6.72769i	0.166996	−	0.289246i	−0.770366	−	0.637602i	$-0.779927\pi$
$541$	3.88423	−	6.72769i	0.166996	−	0.289246i	0.937362	+	0.348356i	$0.113260\pi$
$542$		0			0
$543$		−	1.23349i		−	0.0529341i
$544$		0			0
$545$	−9.41957	−	5.43839i	−0.403490	−	0.232955i
$546$		0			0
$547$	−1.66939	+	2.89147i	−0.0713781	+	0.123631i	−0.899506	−	0.436909i	$-0.856073\pi$
$547$	−1.66939	+	2.89147i	−0.0713781	+	0.123631i	0.828127	+	0.560540i	$0.189406\pi$
$548$		0			0
$549$	4.69049	+	8.12417i	0.200185	+	0.346731i
$550$		0			0
$551$	25.9424	−	2.50657i	1.10518	−	0.106783i
$552$		0			0
$553$	0.715263	−	0.412957i	0.0304161	−	0.0175607i
$554$		0			0
$555$	−6.57286	−	3.79484i	−0.279002	−	0.161082i
$556$		0			0
$557$	1.47191	−	2.54942i	0.0623668	−	0.108022i	−0.833156	−	0.553038i	$-0.813468\pi$
$557$	1.47191	−	2.54942i	0.0623668	−	0.108022i	0.895523	+	0.445015i	$0.146802\pi$
$558$		0			0
$559$	30.7534			1.30073
$560$		0			0
$561$	−10.4886	−	6.05560i	−0.442829	−	0.255668i
$562$		0			0
$563$	−40.6625			−1.71372			−0.856860	−	0.515549i	$-0.827588\pi$
$563$	−40.6625			−1.71372			−0.856860	+	0.515549i	$0.827588\pi$
$564$		0			0
$565$	−2.47716	+	1.43019i	−0.104215	+	0.0601684i
$566$		0			0
$567$	−0.0628953	+	0.0363126i	−0.00264136	+	0.00152499i
$568$		0			0
$569$		−	11.0984i		−	0.465271i	−0.972564	−	0.232635i	$-0.925265\pi$
$569$		−	11.0984i		−	0.465271i	0.972564	−	0.232635i	$-0.0747349\pi$
$570$		0			0
$571$			31.4703i			1.31699i	0.752584	+	0.658496i	$0.228807\pi$
$571$			31.4703i			1.31699i	−0.752584	+	0.658496i	$0.771193\pi$
$572$		0			0
$573$	17.4323	−	10.0646i	0.728246	−	0.420453i
$574$		0			0
$575$	19.7932	−	11.4276i	0.825433	−	0.476564i
$576$		0			0
$577$	−0.0700151			−0.00291477			−0.00145738	−	0.999999i	$-0.500464\pi$
$577$	−0.0700151			−0.00291477			−0.00145738	+	0.999999i	$0.500464\pi$
$578$		0			0
$579$	−8.89392	−	5.13491i	−0.369619	−	0.213399i
$580$		0			0
$581$	−0.820535			−0.0340415
$582$		0			0
$583$	9.26602	−	16.0492i	0.383759	−	0.664690i
$584$		0			0
$585$	1.71009	+	0.987318i	0.0707033	+	0.0408206i
$586$		0			0
$587$	10.4649	−	6.04191i	0.431933	−	0.249376i	−0.268237	−	0.963353i	$-0.586441\pi$
$587$	10.4649	−	6.04191i	0.431933	−	0.249376i	0.700170	+	0.713977i	$0.253108\pi$
$588$		0			0
$589$	−2.45107	+	1.74955i	−0.100995	+	0.0720888i
$590$		0			0
$591$	13.8371	+	23.9665i	0.569182	+	0.985852i
$592$		0			0
$593$	3.11772	−	5.40005i	0.128029	−	0.221754i	−0.794884	−	0.606762i	$-0.792468\pi$
$593$	3.11772	−	5.40005i	0.128029	−	0.221754i	0.922913	+	0.385008i	$0.125801\pi$
$594$		0			0
$595$	−0.302543	−	0.174673i	−0.0124031	−	0.00716091i
$596$		0			0
$597$		−	19.6807i		−	0.805479i
$598$		0			0
$599$	−6.27446	+	10.8677i	−0.256367	+	0.444041i	−0.965266	−	0.261269i	$-0.915859\pi$
$599$	−6.27446	+	10.8677i	−0.256367	+	0.444041i	0.708899	+	0.705310i	$0.249192\pi$
$600$		0			0
$601$			24.3511i			0.993302i	0.867950	+	0.496651i	$0.165437\pi$
$601$			24.3511i			0.993302i	−0.867950	+	0.496651i	$0.834563\pi$
$602$		0			0
$603$	1.61637	+	2.79963i	0.0658236	+	0.114010i
$604$		0			0
$605$	−2.76622	−	4.79124i	−0.112463	−	0.194792i
$606$		0			0
$607$	11.8367			0.480435			0.240218	−	0.970719i	$-0.422781\pi$
$607$	11.8367			0.480435			0.240218	+	0.970719i	$0.422781\pi$
$608$		0			0
$609$	0.434250			0.0175967
$610$		0			0
$611$	−5.43527	−	9.41416i	−0.219887	−	0.380856i
$612$		0			0
$613$	−21.6932	−	37.5736i	−0.876178	−	1.51759i	−0.855502	−	0.517799i	$-0.826752\pi$
$613$	−21.6932	−	37.5736i	−0.876178	−	1.51759i	−0.0206757	−	0.999786i	$-0.506582\pi$
$614$		0			0
$615$		−	0.846615i		−	0.0341388i
$616$		0			0
$617$	13.7532	−	23.8212i	0.553683	−	0.959007i	−0.444322	−	0.895867i	$-0.646555\pi$
$617$	13.7532	−	23.8212i	0.553683	−	0.959007i	0.998005	−	0.0631397i	$-0.0201114\pi$
$618$		0			0
$619$			44.0057i			1.76874i	0.466787	+	0.884370i	$0.345411\pi$
$619$			44.0057i			1.76874i	−0.466787	+	0.884370i	$0.654589\pi$
$620$		0			0
$621$	4.39446	+	2.53714i	0.176344	+	0.101812i
$622$		0			0
$623$	0.296321	−	0.513244i	0.0118719	−	0.0205627i
$624$		0			0
$625$	−8.90386	−	15.4219i	−0.356154	−	0.616877i
$626$		0			0
$627$	3.20256	−	7.03349i	0.127898	−	0.280890i
$628$		0			0
$629$	−63.7599	+	36.8118i	−2.54227	+	1.46778i
$630$		0			0
$631$	30.0724	+	17.3623i	1.19717	+	0.691184i	0.959922	−	0.280267i	$-0.0904229\pi$
$631$	30.0724	+	17.3623i	1.19717	+	0.691184i	0.237243	+	0.971450i	$0.423756\pi$
$632$		0			0
$633$	9.80726	−	16.9867i	0.389804	−	0.675160i
$634$		0			0
$635$	8.83375			0.350557
$636$		0			0
$637$	16.9864	+	9.80709i	0.673025	+	0.388571i
$638$		0			0
$639$	3.80558			0.150546
$640$		0			0
$641$	15.7958	−	9.11971i	0.623897	−	0.360207i	−0.154488	−	0.987995i	$-0.549373\pi$
$641$	15.7958	−	9.11971i	0.623897	−	0.360207i	0.778385	+	0.627788i	$0.216039\pi$
$642$		0			0
$643$	7.56336	−	4.36671i	0.298270	−	0.172206i	−0.343396	−	0.939191i	$-0.611577\pi$
$643$	7.56336	−	4.36671i	0.298270	−	0.172206i	0.641665	+	0.766985i	$0.278244\pi$
$644$		0			0
$645$			7.72292i			0.304090i
$646$		0			0
$647$		−	34.5327i		−	1.35762i	−0.734314	−	0.678810i	$-0.762496\pi$
$647$		−	34.5327i		−	1.35762i	0.734314	−	0.678810i	$-0.237504\pi$
$648$		0			0
$649$	−22.2410	+	12.8408i	−0.873035	+	0.504047i
$650$		0			0
$651$	−0.0434524	+	0.0250872i	−0.00170303	+	0.000983246i
$652$		0			0
$653$	−2.14048			−0.0837633			−0.0418816	−	0.999123i	$-0.513335\pi$
$653$	−2.14048			−0.0837633			−0.0418816	+	0.999123i	$0.513335\pi$
$654$		0			0
$655$	−8.87893	−	5.12625i	−0.346929	−	0.200299i
$656$		0			0
$657$	−10.9222			−0.426116
$658$		0			0
$659$	−3.66647	+	6.35051i	−0.142825	+	0.247381i	−0.928560	−	0.371184i	$-0.878952\pi$
$659$	−3.66647	+	6.35051i	−0.142825	+	0.247381i	0.785734	+	0.618564i	$0.212285\pi$
$660$		0			0
$661$	20.4420	+	11.8022i	0.795101	+	0.459052i	0.841755	−	0.539859i	$-0.181523\pi$
$661$	20.4420	+	11.8022i	0.795101	+	0.459052i	−0.0466544	+	0.998911i	$0.514856\pi$
$662$		0			0
$663$	16.5886	−	9.57746i	0.644250	−	0.371958i
$664$		0			0
$665$	0.0923775	−	0.202880i	0.00358225	−	0.00786737i
$666$		0			0
$667$	−15.1704	−	26.2759i	−0.587400	−	1.01741i
$668$		0			0
$669$	11.7774	−	20.3991i	0.455342	−	0.788675i
$670$		0			0
$671$	−14.4041	−	8.31619i	−0.556063	−	0.321043i
$672$		0			0
$673$			34.1646i			1.31695i	0.752603	+	0.658474i	$0.228798\pi$
$673$			34.1646i			1.31695i	−0.752603	+	0.658474i	$0.771202\pi$
$674$		0			0
$675$	2.25206	−	3.90068i	0.0866819	−	0.150137i
$676$		0			0
$677$			6.65640i			0.255826i	0.991785	+	0.127913i	$0.0408279\pi$
$677$			6.65640i			0.255826i	−0.991785	+	0.127913i	$0.959172\pi$
$678$		0			0
$679$	0.289676	+	0.501734i	0.0111168	+	0.0192548i
$680$		0			0
$681$	1.46242	+	2.53298i	0.0560399	+	0.0970639i
$682$		0			0
$683$	−29.2564			−1.11947			−0.559733	−	0.828673i	$-0.689096\pi$
$683$	−29.2564			−1.11947			−0.559733	+	0.828673i	$0.689096\pi$
$684$		0			0
$685$	−10.0319			−0.383299
$686$		0			0
$687$	−8.66913	−	15.0154i	−0.330748	−	0.572872i
$688$		0			0
$689$	14.6550	+	25.3832i	0.558312	+	0.967025i
$690$		0			0
$691$		−	16.9501i		−	0.644811i	−0.946602	−	0.322405i	$-0.895509\pi$
$691$		−	16.9501i		−	0.644811i	0.946602	−	0.322405i	$-0.104491\pi$
$692$		0			0
$693$	0.0643819	−	0.111513i	0.00244567	−	0.00423602i
$694$		0			0
$695$			9.92152i			0.376345i
$696$		0			0
$697$	−7.11230	−	4.10629i	−0.269398	−	0.155537i
$698$		0			0
$699$	−5.27035	+	9.12851i	−0.199343	+	0.345272i
$700$		0			0
$701$	14.4425	+	25.0151i	0.545485	+	0.944808i	0.998576	+	0.0533437i	$0.0169879\pi$
$701$	14.4425	+	25.0151i	0.545485	+	0.944808i	−0.453091	+	0.891464i	$0.649679\pi$
$702$		0			0
$703$	−27.2940	−	38.2382i	−1.02941	−	1.44218i
$704$		0			0
$705$	2.36412	−	1.36493i	0.0890380	−	0.0514061i
$706$		0			0
$707$	0.953002	+	0.550216i	0.0358413	+	0.0206930i
$708$		0			0
$709$	12.7331	−	22.0543i	0.478200	−	0.828267i	−0.521487	−	0.853259i	$-0.674623\pi$
$709$	12.7331	−	22.0543i	0.478200	−	0.828267i	0.999688	+	0.0249917i	$0.00795592\pi$
$710$		0			0
$711$	−11.3723			−0.426493
$712$		0			0
$713$	3.03599	+	1.75283i	0.113699	+	0.0656440i
$714$		0			0
$715$	−3.50101			−0.130930
$716$		0			0
$717$	3.66551	−	2.11628i	0.136891	−	0.0790340i
$718$		0			0
$719$	−11.7643	+	6.79215i	−0.438736	+	0.253304i	−0.703061	−	0.711129i	$-0.748184\pi$
$719$	−11.7643	+	6.79215i	−0.438736	+	0.253304i	0.264325	+	0.964434i	$0.414851\pi$
$720$		0			0
$721$		−	0.399452i		−	0.0148764i
$722$		0			0
$723$			0.351832i			0.0130848i
$724$		0			0
$725$	−23.3234	+	13.4658i	−0.866210	+	0.500107i
$726$		0			0
$727$	−7.11240	+	4.10635i	−0.263784	+	0.152296i	−0.626060	−	0.779775i	$-0.715333\pi$
$727$	−7.11240	+	4.10635i	−0.263784	+	0.152296i	0.362275	+	0.932071i	$0.382000\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	64.8792	+	37.4580i	2.39964	+	1.38543i
$732$		0			0
$733$	28.3976			1.04889			0.524445	−	0.851444i	$-0.324273\pi$
$733$	28.3976			1.04889			0.524445	+	0.851444i	$0.324273\pi$
$734$		0			0
$735$	−2.46280	+	4.26569i	−0.0908416	+	0.157342i
$736$		0			0
$737$	−4.96371	−	2.86580i	−0.182841	−	0.105563i
$738$		0			0
$739$	30.2534	−	17.4668i	1.11289	−	0.642528i	0.173314	−	0.984867i	$-0.444552\pi$
$739$	30.2534	−	17.4668i	1.11289	−	0.642528i	0.939577	+	0.342339i	$0.111219\pi$
$740$		0			0
$741$	7.10117	+	9.94857i	0.260868	+	0.365470i
$742$		0			0
$743$	−10.1304	−	17.5464i	−0.371649	−	0.643714i	0.618171	−	0.786044i	$-0.287874\pi$
$743$	−10.1304	−	17.5464i	−0.371649	−	0.643714i	−0.989819	+	0.142330i	$0.954541\pi$
$744$		0			0
$745$	−2.63277	+	4.56010i	−0.0964573	+	0.167069i
$746$		0			0
$747$	9.78453	+	5.64910i	0.357997	+	0.206690i
$748$		0			0
$749$		−	0.825925i		−	0.0301786i
$750$		0			0
$751$	24.4701	−	42.3835i	0.892928	−	1.54660i	0.0565803	−	0.998398i	$-0.481980\pi$
$751$	24.4701	−	42.3835i	0.892928	−	1.54660i	0.836348	−	0.548199i	$-0.184686\pi$
$752$		0			0
$753$			24.3758i			0.888304i
$754$		0			0
$755$	3.52624	+	6.10763i	0.128333	+	0.222279i
$756$		0			0
$757$	−8.15290	−	14.1212i	−0.296322	−	0.513245i	0.678969	−	0.734167i	$-0.262427\pi$
$757$	−8.15290	−	14.1212i	−0.296322	−	0.513245i	−0.975292	+	0.220921i	$0.929094\pi$
$758$		0			0
$759$	−8.99665			−0.326558
$760$		0			0
$761$	40.1681			1.45609			0.728047	−	0.685527i	$-0.240428\pi$
$761$	40.1681			1.45609			0.728047	+	0.685527i	$0.240428\pi$
$762$		0			0
$763$	−0.560881	−	0.971474i	−0.0203052	−	0.0351697i
$764$		0			0
$765$	2.40513	+	4.16581i	0.0869577	+	0.150615i
$766$		0			0
$767$		−	40.6178i		−	1.46662i
$768$		0			0
$769$	26.5649	−	46.0117i	0.957954	−	1.65922i	0.230495	−	0.973073i	$-0.425965\pi$
$769$	26.5649	−	46.0117i	0.957954	−	1.65922i	0.727459	−	0.686151i	$-0.240701\pi$
$770$		0			0
$771$			19.1508i			0.689701i
$772$		0			0
$773$	33.5464	+	19.3680i	1.20658	+	0.696620i	0.962011	−	0.273012i	$-0.0880198\pi$
$773$	33.5464	+	19.3680i	1.20658	+	0.696620i	0.244570	+	0.969632i	$0.421353\pi$
$774$		0			0
$775$	1.55588	−	2.69486i	0.0558887	−	0.0968021i
$776$		0			0
$777$	−0.391376	−	0.677882i	−0.0140405	−	0.0243189i
$778$		0			0
$779$	2.17165	−	4.76939i	0.0778073	−	0.170881i
$780$		0			0
$781$	−5.84329	+	3.37363i	−0.209089	+	0.120718i
$782$		0			0
$783$	−5.17824	−	2.98966i	−0.185055	−	0.106842i
$784$		0			0
$785$	3.53639	−	6.12520i	0.126219	−	0.218618i
$786$		0			0
$787$	25.7284			0.917119			0.458560	−	0.888664i	$-0.348366\pi$
$787$	25.7284			0.917119			0.458560	+	0.888664i	$0.348366\pi$
$788$		0			0
$789$	2.68676	+	1.55120i	0.0956511	+	0.0552242i
$790$		0			0
$791$	−0.295001			−0.0104890
$792$		0			0
$793$	22.7813	−	13.1528i	0.808987	−	0.467069i
$794$		0			0
$795$	−6.37434	+	3.68023i	−0.226075	+	0.130524i
$796$		0			0
$797$			17.5541i			0.621798i	0.950443	+	0.310899i	$0.100630\pi$
$797$			17.5541i			0.621798i	−0.950443	+	0.310899i	$0.899370\pi$
$798$		0			0
$799$		−	26.4809i		−	0.936826i
$800$		0			0
$801$	−7.06701	+	4.08014i	−0.249701	+	0.144165i
$802$		0			0
$803$	16.7705	−	9.68247i	0.591819	−	0.341687i
$804$		0			0
$805$	−0.259508			−0.00914645
$806$		0			0
$807$	10.4435	+	6.02956i	0.367629	+	0.212251i
$808$		0			0
$809$	29.2175			1.02723			0.513616	−	0.858020i	$-0.328306\pi$
$809$	29.2175			1.02723			0.513616	+	0.858020i	$0.328306\pi$
$810$		0			0
$811$	−7.79841	+	13.5072i	−0.273839	+	0.474303i	−0.969842	−	0.243736i	$-0.921627\pi$
$811$	−7.79841	+	13.5072i	−0.273839	+	0.474303i	0.696003	+	0.718039i	$0.254960\pi$
$812$		0			0
$813$	7.43530	+	4.29277i	0.260767	+	0.150554i
$814$		0			0
$815$	0.493322	−	0.284820i	0.0172803	−	0.00997680i
$816$		0			0
$817$	−19.8100	+	43.5069i	−0.693064	+	1.52211i
$818$		0			0
$819$	0.101826	+	0.176367i	0.00355808	+	0.00616277i
$820$		0			0
$821$	20.5697	−	35.6278i	0.717888	−	1.24342i	−0.243947	−	0.969789i	$-0.578442\pi$
$821$	20.5697	−	35.6278i	0.717888	−	1.24342i	0.961835	−	0.273630i	$-0.0882244\pi$
$822$		0			0
$823$	−34.4865	−	19.9108i	−1.20213	−	0.694047i	−0.241098	−	0.970501i	$-0.577508\pi$
$823$	−34.4865	−	19.9108i	−1.20213	−	0.694047i	−0.961027	+	0.276453i	$0.910841\pi$
$824$		0			0
$825$			7.98576i			0.278028i
$826$		0			0
$827$	−7.90231	+	13.6872i	−0.274790	+	0.475951i	−0.970082	−	0.242777i	$-0.921942\pi$
$827$	−7.90231	+	13.6872i	−0.274790	+	0.475951i	0.695292	+	0.718727i	$0.255275\pi$
$828$		0			0
$829$			9.83528i			0.341593i	0.985306	+	0.170797i	$0.0546341\pi$
$829$			9.83528i			0.341593i	−0.985306	+	0.170797i	$0.945366\pi$
$830$		0			0
$831$	−3.75279	−	6.50002i	−0.130183	−	0.225483i
$832$		0			0
$833$	23.8903	+	41.3792i	0.827750	+	1.43370i
$834$		0			0
$835$	−5.38268			−0.186275
$836$		0			0
$837$	0.690868			0.0238799
$838$		0			0
$839$	9.94373	+	17.2231i	0.343296	+	0.594606i	0.985043	−	0.172311i	$-0.0551233\pi$
$839$	9.94373	+	17.2231i	0.343296	+	0.594606i	−0.641747	+	0.766917i	$0.721790\pi$
$840$		0			0
$841$	3.37611	+	5.84759i	0.116418	+	0.201641i
$842$		0			0
$843$			1.90964i			0.0657715i
$844$		0			0
$845$	−1.80863	+	3.13265i	−0.0622189	+	0.107766i
$846$		0			0
$847$		−	0.570581i		−	0.0196054i
$848$		0			0
$849$	23.5620	+	13.6035i	0.808644	+	0.466871i
$850$		0			0
$851$	−27.3452	+	47.3633i	−0.937381	+	1.62359i
$852$		0			0
$853$	−16.1443	−	27.9627i	−0.552769	−	0.957424i	−0.998073	−	0.0620446i	$-0.980238\pi$
$853$	−16.1443	−	27.9627i	−0.552769	−	0.957424i	0.445304	−	0.895379i	$-0.353095\pi$
$854$		0			0
$855$	−2.49832	+	1.78327i	−0.0854409	+	0.0609867i
$856$		0			0
$857$	10.6837	−	6.16823i	0.364948	−	0.210703i	−0.306301	−	0.951935i	$-0.599091\pi$
$857$	10.6837	−	6.16823i	0.364948	−	0.210703i	0.671249	+	0.741232i	$0.265758\pi$
$858$		0			0
$859$	−16.4923	−	9.52185i	−0.562711	−	0.324881i	0.191522	−	0.981488i	$-0.438658\pi$
$859$	−16.4923	−	9.52185i	−0.562711	−	0.324881i	−0.754233	+	0.656607i	$0.771991\pi$
$860$		0			0
$861$	0.0436572	−	0.0756166i	0.00148784	−	0.00257701i
$862$		0			0
$863$	−15.8003			−0.537850			−0.268925	−	0.963161i	$-0.586668\pi$
$863$	−15.8003			−0.537850			−0.268925	+	0.963161i	$0.586668\pi$
$864$		0			0
$865$	−6.93302	−	4.00278i	−0.235730	−	0.136099i
$866$		0			0
$867$	29.6618			1.00737
$868$		0			0
$869$	17.4616	−	10.0815i	0.592344	−	0.341990i
$870$		0			0
$871$	7.85055	−	4.53252i	0.266006	−	0.153579i
$872$		0			0
$873$		−	7.97729i		−	0.269990i
$874$		0			0
$875$			0.486057i			0.0164317i
$876$		0			0
$877$	−13.7280	+	7.92586i	−0.463561	+	0.267637i	−0.713541	−	0.700614i	$-0.752910\pi$
$877$	−13.7280	+	7.92586i	−0.463561	+	0.267637i	0.249979	+	0.968251i	$0.419576\pi$
$878$		0			0
$879$	9.61145	−	5.54917i	0.324186	−	0.187169i
$880$		0			0
$881$	−40.9662			−1.38019			−0.690093	−	0.723721i	$-0.742430\pi$
$881$	−40.9662			−1.38019			−0.690093	+	0.723721i	$0.742430\pi$
$882$		0			0
$883$	−16.8948	−	9.75421i	−0.568555	−	0.328255i	0.188017	−	0.982166i	$-0.439794\pi$
$883$	−16.8948	−	9.75421i	−0.568555	−	0.328255i	−0.756572	+	0.653910i	$0.773127\pi$
$884$		0			0
$885$	10.2001			0.342873
$886$		0			0
$887$	5.57203	−	9.65104i	0.187090	−	0.324050i	−0.757188	−	0.653196i	$-0.773428\pi$
$887$	5.57203	−	9.65104i	0.187090	−	0.324050i	0.944279	+	0.329146i	$0.106761\pi$
$888$		0			0
$889$	0.788998	+	0.455528i	0.0264621	+	0.0152779i
$890$		0			0
$891$	−1.53545	+	0.886495i	−0.0514396	+	0.0296987i
$892$		0			0
$893$	16.8194	−	1.62510i	0.562840	−	0.0543818i
$894$		0			0
$895$	−1.67288	−	2.89752i	−0.0559183	−	0.0968533i
$896$		0			0
$897$	7.11450	−	12.3227i	0.237546	−	0.411442i
$898$		0			0
$899$	−3.57748	−	2.06546i	−0.119316	−	0.0688869i
$900$		0			0
$901$			71.4000i			2.37868i
$902$		0			0
$903$	−0.398246	+	0.689782i	−0.0132528	+	0.0229545i
$904$		0			0
$905$		−	0.868606i		−	0.0288735i
$906$		0			0
$907$	5.65089	+	9.78763i	0.187635	+	0.324993i	0.944461	−	0.328623i	$-0.106585\pi$
$907$	5.65089	+	9.78763i	0.187635	+	0.324993i	−0.756826	+	0.653616i	$0.773251\pi$
$908$		0			0
$909$	−7.57609	−	13.1222i	−0.251283	−	0.435235i
$910$		0			0
$911$	53.3381			1.76717			0.883585	−	0.468270i	$-0.155123\pi$
$911$	53.3381			1.76717			0.883585	+	0.468270i	$0.155123\pi$
$912$		0			0
$913$	−20.0316			−0.662949
$914$		0			0
$915$	3.30298	+	5.72093i	0.109193	+	0.189128i
$916$		0			0
$917$	−0.528689	−	0.915716i	−0.0174589	−	0.0302396i
$918$		0			0
$919$		−	59.7213i		−	1.97002i	−0.172491	−	0.985011i	$-0.555181\pi$
$919$		−	59.7213i		−	1.97002i	0.172491	−	0.985011i	$-0.444819\pi$
$920$		0			0
$921$	3.95490	−	6.85009i	0.130318	−	0.225718i
$922$		0			0
$923$		−	10.6714i		−	0.351253i
$924$		0			0
$925$	42.0413	+	24.2726i	1.38231	+	0.798078i
$926$		0			0
$927$	−2.75009	+	4.76330i	−0.0903249	+	0.156447i
$928$		0			0
$929$	−15.5602	−	26.9511i	−0.510514	−	0.884235i	−0.999926	−	0.0121828i	$-0.996122\pi$
$929$	−15.5602	−	26.9511i	−0.510514	−	0.884235i	0.489412	−	0.872053i	$-0.337211\pi$
$930$		0			0
$931$	−24.8160	+	17.7134i	−0.813312	+	0.580532i
$932$		0			0
$933$	18.1955	−	10.5052i	0.595694	−	0.343924i
$934$		0			0
$935$	−7.38593	−	4.26427i	−0.241546	−	0.139457i
$936$		0			0
$937$	−0.985759	+	1.70738i	−0.0322033	+	0.0557778i	−0.881678	−	0.471852i	$-0.843586\pi$
$937$	−0.985759	+	1.70738i	−0.0322033	+	0.0557778i	0.849475	+	0.527630i	$0.176919\pi$
$938$		0			0
$939$	−7.69554			−0.251135
$940$		0			0
$941$	−45.9983	−	26.5572i	−1.49950	−	0.865738i	−0.499503	−	0.866312i	$-0.666484\pi$
$941$	−45.9983	−	26.5572i	−1.49950	−	0.865738i	−1.00000		0.000573531i	$0.999817\pi$
$942$		0			0
$943$	−6.10061			−0.198663
$944$		0			0
$945$	−0.0442900	+	0.0255709i	−0.00144076	+	0.000831821i
$946$		0			0
$947$	5.12227	−	2.95734i	0.166451	−	0.0961007i	−0.414460	−	0.910067i	$-0.636030\pi$
$947$	5.12227	−	2.95734i	0.166451	−	0.0961007i	0.580911	+	0.813967i	$0.302696\pi$
$948$		0			0
$949$			30.6274i			0.994206i
$950$		0			0
$951$			17.9247i			0.581248i
$952$		0			0
$953$	42.6334	−	24.6144i	1.38103	−	0.797338i	0.388748	−	0.921344i	$-0.372908\pi$
$953$	42.6334	−	24.6144i	1.38103	−	0.797338i	0.992281	+	0.124006i	$0.0395742\pi$
$954$		0			0
$955$	12.2756	−	7.08733i	0.397229	−	0.229341i
$956$		0			0
$957$	10.6013			0.342690
$958$		0			0
$959$	−0.896012	−	0.517313i	−0.0289337	−	0.0167049i
$960$		0			0
$961$	−30.5227			−0.984603
$962$		0			0
$963$	−5.68621	+	9.84880i	−0.183235	+	0.317373i
$964$		0			0
$965$	−6.26298	−	3.61593i	−0.201612	−	0.116401i
$966$		0			0
$967$	12.9601	−	7.48250i	0.416768	−	0.240621i	−0.276926	−	0.960891i	$-0.589316\pi$
$967$	12.9601	−	7.48250i	0.416768	−	0.240621i	0.693694	+	0.720270i	$0.255982\pi$
$968$		0			0
$969$	2.86358	+	29.6374i	0.0919913	+	0.952090i
$970$		0			0
$971$	7.57514	+	13.1205i	0.243098	+	0.421058i	0.961595	−	0.274472i	$-0.0885030\pi$
$971$	7.57514	+	13.1205i	0.243098	+	0.421058i	−0.718497	+	0.695530i	$0.755170\pi$
$972$		0			0
$973$	−0.511621	+	0.886153i	−0.0164018	+	0.0284088i
$974$		0			0
$975$	−10.9381	−	6.31509i	−0.350298	−	0.202245i
$976$		0			0
$977$			49.2334i			1.57511i	0.616241	+	0.787557i	$0.288655\pi$
$977$			49.2334i			1.57511i	−0.616241	+	0.787557i	$0.711345\pi$
$978$		0			0
$979$	7.23405	−	12.5297i	0.231201	−	0.400452i
$980$		0			0
$981$			15.4459i			0.493149i
$982$		0			0
$983$	21.4667	+	37.1814i	0.684682	+	1.18590i	0.973537	+	0.228531i	$0.0733921\pi$
$983$	21.4667	+	37.1814i	0.684682	+	1.18590i	−0.288855	+	0.957373i	$0.593275\pi$
$984$		0			0
$985$	9.74389	+	16.8769i	0.310466	+	0.537743i
$986$		0			0
$987$	0.281540			0.00896150
$988$		0			0
$989$	55.6504			1.76958
$990$		0			0
$991$	−7.83230	−	13.5659i	−0.248801	−	0.430937i	0.714392	−	0.699746i	$-0.246703\pi$
$991$	−7.83230	−	13.5659i	−0.248801	−	0.430937i	−0.963194	+	0.268809i	$0.913370\pi$
$992$		0			0
$993$	12.6752	+	21.9541i	0.402235	+	0.696692i
$994$		0			0
$995$		−	13.8589i		−	0.439357i
$996$		0			0
$997$	−19.5704	+	33.8969i	−0.619801	+	1.07353i	0.369721	+	0.929143i	$0.379453\pi$
$997$	−19.5704	+	33.8969i	−0.619801	+	1.07353i	−0.989522	+	0.144384i	$0.953880\pi$
$998$		0			0
$999$			10.7779i			0.340999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1824.2.bb.a.31.9	✓	40
4.3	odd	2		1824.2.bb.b.31.9	yes	40
19.8	odd	6		1824.2.bb.b.1471.9	yes	40
76.27	even	6	inner	1824.2.bb.a.1471.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1824.2.bb.a.31.9	✓	40	1.1	even	1	trivial
1824.2.bb.a.1471.9	yes	40	76.27	even	6	inner
1824.2.bb.b.31.9	yes	40	4.3	odd	2
1824.2.bb.b.1471.9	yes	40	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1824 = 2^{5} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1824.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.352093 - 0.609843i) q^{5} -0.0726253i q^{7} +(-0.500000 + 0.866025i) q^{9} -1.77299i q^{11} +(2.42846 + 1.40207i) q^{13} +(-0.352093 + 0.609843i) q^{15} +(3.41547 + 5.91577i) q^{17} +(-3.54782 + 2.53239i) q^{19} +(-0.0628953 + 0.0363126i) q^{21} +(4.39446 + 2.53714i) q^{23} +(2.25206 - 3.90068i) q^{25} +1.00000 q^{27} +(-5.17824 - 2.98966i) q^{29} +0.690868 q^{31} +(-1.53545 + 0.886495i) q^{33} +(-0.0442900 + 0.0255709i) q^{35} +10.7779i q^{37} -2.80414i q^{39} +(-1.04119 + 0.601130i) q^{41} +(9.49783 - 5.48357i) q^{43} +0.704186 q^{45} +(-3.35724 - 1.93830i) q^{47} +6.99473 q^{49} +(3.41547 - 5.91577i) q^{51} +(9.05207 + 5.22621i) q^{53} +(-1.08125 + 0.624257i) q^{55} +(3.96702 + 1.80630i) q^{57} +(-7.24248 - 12.5443i) q^{59} +(4.69049 - 8.12417i) q^{61} +(0.0628953 + 0.0363126i) q^{63} -1.97464i q^{65} +(1.61637 - 2.79963i) q^{67} -5.07429i q^{69} +(-1.90279 - 3.29573i) q^{71} +(5.46110 + 9.45890i) q^{73} -4.50412 q^{75} -0.128764 q^{77} +(5.68613 + 9.84867i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.2982i q^{83} +(2.40513 - 4.16581i) q^{85} +5.97932i q^{87} +(7.06701 + 4.08014i) q^{89} +(0.101826 - 0.176367i) q^{91} +(-0.345434 - 0.598309i) q^{93} +(2.79352 + 1.27197i) q^{95} +(-6.90853 + 3.98864i) q^{97} +(1.53545 + 0.886495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 20 q^{3} - 20 q^{9} - 12 q^{13} + 8 q^{19} - 12 q^{21} - 20 q^{25} + 40 q^{27} - 40 q^{31} + 24 q^{41} - 12 q^{43} + 24 q^{47} - 16 q^{49} - 24 q^{53} - 4 q^{57} - 4 q^{61} + 12 q^{63} + 4 q^{67}+ \cdots - 24 q^{97}+O(q^{100}) \) 40 * q - 20 * q^3 - 20 * q^9 - 12 * q^13 + 8 * q^19 - 12 * q^21 - 20 * q^25 + 40 * q^27 - 40 * q^31 + 24 * q^41 - 12 * q^43 + 24 * q^47 - 16 * q^49 - 24 * q^53 - 4 * q^57 - 4 * q^61 + 12 * q^63 + 4 * q^67 + 32 * q^71 + 4 * q^73 + 40 * q^75 + 32 * q^77 + 4 * q^79 - 20 * q^81 - 16 * q^85 - 48 * q^89 + 12 * q^91 + 20 * q^93 + 56 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more